Discharging Zakaat And Interest Money Combined

Both the funds are dissimilar in the sight of Shariah and, therefore, dealt dissimilarly. Zakaat wealth is Halaal/pure while the interest amount is an Haraam/abominated wealth. The former is discharged with the intention of reward and the latter without the intention of reward. Therefore, one should not combine them but rather discharge them separately regardless of their recipients being from the same category (interest money can only be given to people eligible to receive Zakaat).

In conclusion yes, the interest will have to be removed each time it accumulates and discharged accordingly to the poor without any intention of reward.